Answer:
See below.
What makes The Iliad and The Odyssey such important pieces of literature?
Because they are two of only three outstanding works of literature produced in the Ancient World (the third being the Bible) (pre-5th c. BCE). Nothing comes close to it. People all across the world still want to read them because they are so brilliantly written, even though they are like night and day in comparison.
As the first significant author from the West or Europe, Homer was the most significant and early of the Greek and Roman writers. Without knowing his poems, Greeks and Romans didn't believe themselves to be learned. Alexander the Great took an annotated copy of the Iliad with him wherever he went and kept it under his pillow because he thought it was a book that might teach him the art of battle. Aristotle had done this for him. Through the teachings from his two outstanding poems, his effect was felt not only on literary but also on ethics and morals.
Except for the Hebrews, authors did not use prose throughout the ancient world. They produced poetry instead (myth), and their style is referred to as "epic" or "epic poetry." The "Epic of Gilgamesh" is the beginning of epic poetry, but Homer's "Iliad" and "Odyssey" are where its position and significance in history are established. Homer lays forth the whole structure of the epic poem. The Homeric or Epic simile, rich and graphic depictions, in-depth character development, monologues, and noble characters distinguish it from the Epic of Gilgamesh. Despite being fiction, it describes events as if they were historical. However, the Greeks and Romans believed they were genuine.
He was read and imitated by all notable epic writers, including Hesiod, Apollonius, Ovid, Lucan, and Statius. Even Virgil (70 BCE–19 BC), who wrote the "Aeneid" (Latin: Aeneis), the greatest epic poetry of the Roman Empire, took the name of the work from a Trojan named Aeneis in Homer's Iliad, who flees Troy and settles in Italy to create Rome. The Aeneid served as the inspiration for Milton's "Paradise Lost" and was read and widely known by every notable Medieval and Renaissance author. And Homer’s Iliad and Odyssey are still popular books to this day. Thus, Homer's contribution to Western literature was significant.
Along with shaping literature's epic structure or style, only the Hebrews had done this previously in their historical accounts of events. He also included moral teachings into the narrative. The character traits that the Iliad and Odyssey commend are traits that the Greeks valued highly, while the character traits that they criticize are traits that the Greeks despised. His epics therefore had the most impact on ancient Greek society and learning. Homer was the one who "educated Greece," according to Plato. Plato recognized the enduring influence Homer had on his people, but he also saw the shortcomings that persisted. In many respects, Plato's Republic was a reaction to Homer and the Greece that he portrayed.